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4 years ago

Solve the system by substitution -x - y - z = -8 -4x + 4y + 5z = 7 2x + 2z = 4

Mathematics

2 answers:

zhuklara [117]4 years ago

7 0

Answer: The required solution of the given system is

x = 3, y = 6 and z = -1.

Step-by-step explanation: We are given to solve the following system of equations by the method of substitution :

$-x-y-z=-8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-4x+4y+5z=7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\2x+2z=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

From equation (iii), we have

$2x+2z=4\\\\\Rightarrow x+z=2\\\\\Rightarrow x=2-z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)$

Substituting the value of x from equation (iv) in equations (i) and (ii), we get

$-(2-z)-y-z=-8\\\\\Rightarrow 2-z+y+z=8\\\\\Rightarrow 2+y=8\\\\\Rightarrow y=8-2\\\\\Rightarrow y=6$

and

$-4(2-z)+4y+5z=7\\\\\Rightarrow -8+4z+4\times6+5z=7\\\\\Rightarrow 9z+16=7\\\\\Rightarrow 9z=-9\\\\\Rightarrow z=-\dfrac{9}{9}\\\\\Rightarrow z=-1.$

From equation (iii), we get

$2x+2(-1)=4\\\\\Rightarrow 2x=6\\\\\Rightarrow x=\dfrac{6}{2}\\\\\Rightarrow x=3.$

Thus, the required solution of the given system is

x = 3, y = 6 and z = -1.

gulaghasi [49]4 years ago

5 0

Answer: 14

Step-by-step explanation:

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Write 0.614¯¯¯ as a fraction in simplest form.

Verizon [17]

Answer:

307/500

Step-by-step explanation:

307 is a prime number.

The way to find this out is to take 0.614 and multiply it by 1,000 because then it will be a natural number. 0.614*1,000=614.

now you take 614/1,000 because that's what you multiplied it by and simplify it.

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3 years ago

How to solve the problem

morpeh [17]

Might be better if you typed the question

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4 years ago

Given s left parenthesis t right parenthesis equals 5 t squared plus 5 ts(t)=5t2+5t, find

finlep [7]

Answer:

The velocity function is $v(t)=10t+5$ .

The acceleration function is $a(t)=10$ .

When t = 44, the velocity is $v(44)=445 \:\frac{ft}{s}$ .

When t = 44, the acceleration is $a(44)=10\: \frac{ft}{s^2}$ .

Step-by-step explanation:

We know that the position function is given by

$s(t)=5t^2+5t$

Velocity is defined as the rate of change of position or the rate of displacement. If you take the derivative of the position function you get the instantaneous velocity function.

$v(t)=\frac{ds}{dt}$

Acceleration is defined as the rate of change of velocity. If you take the derivative of the instantaneous velocity function you get the instantaneous acceleration function.

$a(t)=\frac{dv}{dt}$

The instantaneous velocity function is given by

$v(t)=\frac{d}{dt} s(t)=\frac{d}{dt}(5t^2+5t)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(5t^2\right)+\frac{d}{dt}\left(5t\right)\\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}\\\\v(t)=10t+\frac{d}{dt}\left(5t\right)\\\\\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dt}\left(t\right)=1\\\\v(t)=10t+5$

The instantaneous acceleration function is given by

$a(t)=\frac{dv}{dt} =\frac{d}{dt}(10t+5)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\a(t)=\frac{d}{dt}\left(10t\right)+\frac{d}{dt}\left(5\right)\\\\a(t)=10$

To find the velocity and acceleration when t = 44, we substitute this value into the velocity and acceleration functions

$v(44)=10(44)+5\\v(44)=445 \:\frac{ft}{s}$

$a(44)=10\: \frac{ft}{s^2}$

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4 years ago

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Minchanka [31]

Answer: i think C

Step-by-step explanation: Well the X Value would have to change because if you graphed it it would be a straight line going up which wouldnt pass a through a vertical line.

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3 years ago

The height, h, of a cylinder is 5 units less than 3 times its radius, r. Which expression represents the hight of the cylinder i

jeyben [28]

You can do radius times 3 -5

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4 years ago

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